5
CHALLENGE Sara had some marbles. She got 20 more marbles for her
birthday, and she got 30 marbles at the store. Now Sara has 100 marbles.
How many marbles did she have to start?

Answer:

Distance xy = 11.66 unit (Approx)

Step-by-step explanation:

Given:

x(-7,10)

y(3,4)

Find:

Distance xy

Computation:

Distance = √(x2-x1)²+(y2-y1)²

Distance xy = √(3+7)²+(4-10)²

Distance xy = √ 100 + 36

Distance xy = 11.66 unit (Approx)

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. Anna earns $20 for every 400 envelopes. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

Jason has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table of Anna and Jason we can see that Anna makes more stuffing than Jason for the same number of envelopes.

c) Anna has a savings of $100 initially. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

Therefore from the graph there is a y intercept at 100. That is the earnings starts initially is $100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value of y at x = 0)

For the first graph, the slope is 1/20 with an initial value of 0 while for the second graph the slope is 1/15 with an initial value of 100

D) The trend line pass through the points (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

Answer:

2.333

Step-by-step explanation:

Given that:

Conceded goals: 0,1,2,3,4

Frequency:2,8,4,10,6

Mean(m) = Σ(fx) / Σf

Σfx = (0*2) + (1*8) + (2*4) + (3*10) + (4*6) = 70

Σf = (2 + 8 + 4 + 10 + 6) = 30

Hence,

Mean = 70 / 30

Mean = 2.333

Answer:

g(x) = 1/2x² is the correction option.

Hence, option B is true.

Step-by-step explanation:

Please check the attached graph.

It means when we multiply the parent function by a number 'b' which is less than 1, then the parent function f(x) = x² is vertically compressed by b.

Here, the graph is vertically compressed by 1/2, therefore we conclude that g(x) = 1/2x² is the result of vertical compression of the parent function by 1/2.

Therefore, g(x) = 1/2x² is the correction option.

Hence, option B is true.

Answer:

Function.

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

If we apply the Vertical Line Test to the graph, we can see that each x-value has it's own y-value. Therefore, the graph is a function and not a relation.

Answer:

64

Step-by-step explanation:

v = s^3

v = (4)^3 [4x4x4]

v = 64

Answer:

3 3/4 brick house

Step-by-step explanation:

Total bricks bought = 3/4 of a ton

Each brick house uses = 1/5 of a ton

How many brick house can Jamie complete before they have to order more?

Number of brick house Jamie can complete with the available bricks = Total bricks bought / bricks per house

= 3/4 ÷ 1/5

= 3/4 × 5/1

= 15/4

= 3 3/4 brick house

Jamie will complete 3 3/4 brick house before they have to order more bricks

Final Answer: [tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]

Steps/Reasons/Explanation:

Question: Solve by using the quadratic formula:  [tex]x^{2} - 6x + 7 = 0[/tex].

Step 1: Use the Quadratic Formula.

[tex]x = \frac{6 + \sqrt[2]{2} }{2}, \frac{6 - \sqrt[2]{2} }{2}[/tex]

Step 2: Simplify solutions.

[tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]

~I hope I helped you :)~ The quadratic formulaic is attached in an image.

1. f(x) = x² + x + 4

f(x) = 0

0 = x² + x + 4

-4 = x² + x

2. linear equation

one solution

Answer:

1.05

Step-by-step explanation:

3.5x.30=1.05

Answer:

1.05

Step-by-step explanation:

You will have to multiply if you are trying to find the amount of water in total. So, 0.30*3.5=1.05. So, that would be your answer for the amount of rainfall.

Answer:

c

Step-by-step explanation:

c Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.

y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.

y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.

y less-than one-half x. y less-than-or-equal-to negative one-half x + 2v

The system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

The solution set is given as:

[tex](x,y) = (2,1)[/tex]

The above solution set is true for x + 2y ≤ 4 and 2x - y > 0, and the proof is as follows:

Substitute 2 for x and 1 for y in x + 2y ≤ 4 and 2x - y > 0.

So, we have:

[tex]\mathbf{2 + 2\times1 \le 4 }[/tex]

[tex]\mathbf{2 + 2\le 4 }[/tex]

[tex]\mathbf{4\le 4 }[/tex] --- this is true, because 4 is less than or equal to 4

Also, we have:

[tex]\mathbf{2x - y > 0}[/tex]

[tex]\mathbf{2 \times 2 - 1 > 0}[/tex]

[tex]\mathbf{4 - 1 > 0}[/tex]

[tex]\mathbf{3> 0}[/tex] --- this is also true, because 3 is greater than 0

Hence, the system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

Read more about inequalities at:

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Answer:

10.8 kg

Step-by-step explanation:

w = 80 + 5.4t

At time 0, when he starts the diet, his initial weight is

w = 80 + 5.4(0)

w = 80

80 kg.

After 2 months, t = 2. His weight is

w = 80 + 5.4t

w = 80 + 5.4(2)

w = 80 + 10.8

w = 90.8

90.8 kg.

His gain in 2 months was 90.8 kg - 80 kg = 10.8 kg

Answer: 10.8 kg

The wrestler gains 10.8 kg every 2 months.

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation that models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for t months.

w = 80 + 5.4t

We need to find his weight after 2 months.

At time t = 0, when he starts the diet, the wrestler's initial weight would be,

⇒ w = 80 + 5.4(0)

⇒ w = 80 kg

After 2 months, t = 2 the wrestler's weight  weight would be,

⇒ w = 80 + 5.4(2)

⇒ w = 80 + 10.8

⇒ w = 90.8 kg

We need to find the weight gain in 2 months.

90.8 - 80 = 10.8 kg

Therefore, the wrestler gains 10.8 kg every 2 months.

Learn more about an equation here:

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Answer:

1) The polynomial in standard form is f(x) = x³ - 9·x² + 23·x - 15

2) The polynomial in standard form is f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The polynomial in standard form is f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The polynomial in standard form is f(x) = x² - (5 + √5)·x + 6 + 3·√5

Step-by-step explanation:

Given that that the polynomial is of least degree, we have;

The standard form is the form, f(x) = a·xⁿ + b·xⁿ⁻¹ +...+ c

1) The zeros of the polynomial are x = 5, 3, 1

Which gives the polynomial in factored form as_f(x) = (x - 5)·(x - 3)·(x - 1)

From which we have;

f(x) = (x - 5)·(x - 3)·(x - 1) = (x - 5)·(x² - 4·x + 3) = x³ - 4·x² + 3·x - 5·x² + 20·x - 15

f(x) = x³ - 9·x² + 23·x - 15

The polynomial in standard form is therefore f(x) = x³ - 9·x² + 23·x - 15

2) The zeros of the polynomial are x = 2, 0, 2·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x)·(x - 2·i)

From which we have;

f(x) = (x - 2)·x·(x - 2·i) = (x² - 2·x)·(x - 2·i) = x³ - 2·i·x² + 2·x² + 4·ix

The polynomial in standard form is therefore f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The zeros of the polynomial are x = 2, 1 - 3·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x - 1 - 3·i)

From which we have;

f(x) = (x - 2)·(x - (1 - 3·i)) = x² - x + 3·i·x - 2·x + 2 -6·i = x² + 3·i·x - 3·x + 2 - 6·i

The polynomial in standard form is therefore f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The zeros of the polynomial are x = 3, 2 + √5

Which gives the polynomial in factored form as_f(x) = (x - 3)·(x - (2 + √5))

From which we have;

f(x) = (x - 3)·(x - (2 + √5)) = x² - 2·x - x·√5 - 3·x + 6 + 3·√5

f(x) = x² - 5·x - x·√5 + 6 + 3·√5 = x² - (5 + √5)·x + 6 + 3·√5

The polynomial in standard form is therefore f(x) = x² - (5 + √5)·x + 6 + 3·√5.

Answer:

s = 6 inches

Step-by-step explanation:

Given:

r = 53 inches,

∠S = 6°

∠T = 58°.

Required:

Length of s

Solution:

Use Sine Rule

Thus:

[tex] \frac{s}{Sin(S)} = \frac{r}{Sin(R)} [/tex]

<R = 180 - (58 + 6)

<R = 116°

r = 53 inches,

∠S = 6°

s = ?

Plug in the values

[tex] \frac{s}{Sin(6)} = \frac{53}{Sin(116)} [/tex]

Multiply both sides by Sin(6)

[tex] \frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6) [/tex]

[tex] s = \frac{53 \times Sin(6)}{Sin(116)} [/tex]

[tex] s = 6 inches [/tex] (nearest inch)

Answer:

C. 42 is 6 times as many as 252

Step-by-step explanation:

because 42×6 = 252

Answer: - 6 1/2

Step-by-step explanation:

We should note that:

=-4 - 2 1/2

= -6 1/2

For example, let's assume you owe Bob $4 and then you owe Bill $2 1/2. To calculate the total amount owed, you would have $6 1/2.

Answer:

B). SAS similarity.

Step-by-step explanation:

In Δ WVU & ΔCAB,

UV/CA = 17/34 = 1/2

&

VW/AB = 14/28 = 1/2

∵ UV/CA = VW/AB = 1/2

& ∠V = ∠A (Given)

∵ ΔWVU ≅  ΔCAB   (by SAS similarity)

Answer:

a and c are correct

Step-by-step explanation:

i hoped this helped

Answer:

469.1 yd²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{210}{360}[/tex]

   = π × 16² × [tex]\frac{21}{36}[/tex]

   = 256π × [tex]\frac{7}{12}[/tex]

   ≈ 469.1 yd² ( to 1 dec. place )

Answer:

y = 7

Step-by-step explanation:

Given

4y - 6 = 2y + 8 ( subtract 2y from both sides )

2y - 6 = 8 ( add 6 to both sides )

2y = 14 ( divide both sides by 2 )

y = 7

Answer:

The remainder when 3456 is divided by 7 is 6.

5 is the remainder when 3456 is divided by 7

A division is a process of splitting a specific amount into equal parts.

We need to find the  remainder when 3456 is divided by 7

3456/7

3456:7 is a ratio and 3456/7 is also called as fraction.

The number 3456 is called the numerator or dividend, and the number 7 is called the denominator or divisor.

3456 we can write as 3451+5

3451 is divided by 7 which gives 493.

5 is the remainder when 3456 is divided by 7

Hence, 5 is the remainder when 3456 is divided by 7

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Answer:

The nonlinear system of equations has 4 solutions ⇒ B

Step-by-step explanation:

The number of solutions of a system of equations equal to the number of points of intersection of the graphs of the equations of the system

Let us use this note to solve the question

From the given figure

∵ The nonlinear system of equations represented by two curves and a circle

∵ Each curve intersects the circle into two points

∴ The number of the points of intersection is 4

→ By using the note above

∵ The number of intersection points equal to the number of solutions

∴ The number of solutions is 4

∴ The nonlinear system of equations has 4 solutions

Answer:

cos B = [tex]\frac{7}{25}[/tex]

tan B = [tex]\frac{24}{7}[/tex]

sin B = [tex]\frac{24}{25}[/tex]

Step-by-step explanation:

In the right triangle, there are three sides and 2 acute angles

The trigonometry functions of one of the acute angles Ф are

In Δ ACB

∵ ∠C is the right angle

∴ AB is the hypotenuse

∵ AC is the opposite side of ∠B ⇒ leg1

∵ CB is the adjacent side of ∠B ⇒ leg2

→ By using the ratios above

∴ cos B = [tex]\frac{CB}{AB}[/tex] , tan B = [tex]\frac{AC}{CB}[/tex] , sin B = [tex]\frac{AC}{AB}[/tex]

∵ CB = 7, AB = 25, AC = 24

∴ cos B = [tex]\frac{7}{25}[/tex]

∴ tan B = [tex]\frac{24}{7}[/tex]

∴ sin B = [tex]\frac{24}{25}[/tex]

Answer:

30

Step-by-step explanation:

I asked the my math tutor lol

You can see all answers in the picture

Answer:

9 books each

Step-by-step explanation:

Answer:

1/4n - 16 =

1/4(n - 64)

Step-by-step explanation:

Two expression are said to be equivalent, if after substituting the value of variable by any constant the numerical value of both original expression and equivalent expression are same.

Answers:

plus all rounded so i don't cuffuse anyone

Answer:

m=1

c=7

I hope it will be useful.